In a cast-iron skillet over medium heat, cook burger patty until you see juices form on top, about 5 to 6 minutes.
Then, flip the burger and top with half the cheese and cook another 5 to 6 minutes, or until patty reaches desired doneness. Remove to a plate and keep warm.
In the same skillet, pan-toast the bread, a couple minutes per side, until golden on both sides.
Once you flip each slice to toast the second side, spread pesto on one side of each slice of bread, then top one slice with the rest of the cheese to melt. Lower heat if you need to.
Top one slice of bread with the cooked patty, then top with tomato and olive tapenade and baby spinach, then top with the other slice of bread and serve warm.